Can Blender be used to create a physics based game without programming?
Blender's game engine uses a node concept for "wiring" game functionality which are called logic bricks. You can get more advanced functionality with programming in Python, but the logic bricks can do what you want if you want to avoid the programming. So yes, you can create a game without programming knowledge using Blender's game engine.

The Intro to BGE on the BlenderWiki ( http://wiki.blender.org/index.php/User:Sculptorjim/Game_Engine ) is pretty detailed on how to work with BGE and logic bricks. Blendswap also has an example with physics that you could start off with: http://www.blendswap.com/blends/view/73536 

I know of one person, SolarLune, that has been working with the BGE for quite a while, and he's got quite a few videos up concerning it if you want some tips and tricks. He just did a recent video on why he uses BGE:
youtube.com/watch?v=8ZJEupWdf30

Unity would require programming in C# (or Javascript).